Physics and Astronomy
8 years ago

Unlocking Chaos: New Conditions for Predicting Chaotic Behavior in Systems

Three Conditions Lyapunov Exponents Should Satisfy
Jingjun Lou, Shijian Zhu

Paper Summary

Related papers

Theme background image
Physics and Astronomy
5 years ago

Detect chaos in systems with new method: Lyapunov Exponents approximation unveiled!

Chaos Synchronization
Model Predictive Control
Port-Hamiltonian Control
Theme background image
Mathematics
5 years ago

Uniform limit dynamical systems reveal hidden patterns in complex behaviors.

Dynamical Systems
Planar Bifurcations
Chaos Synchronization
Theme background image
Engineering
8 years ago

New research paves the way for more stable and efficient systems.

Networked Control
Distributed Control
Port-Hamiltonian Control

The article discusses three conditions that Lyapunov exponents should meet in a chaotic system. Positive Lyapunov exponent alone doesn't guarantee chaos. The other two conditions are: any system without a fixed point has at least one zero exponent, and any dissipative system has at least one negative exponent. A MATLAB scheme was used to compute Lyapunov exponents in the Duffing system with nonlinearity.